365 Days of Earrings

Friday, February 4, 2011

Hyperbolic Eccentricity

Today I wore the earrings I bought at the Smithsonian’s Hyperbolic Crochet Coral Reef exhibit last month. Having not studied the hyperbola in 40 years (9th grade Algebra II), I enjoyed exploring it a bit on the web. The word origins are especially delightful to me:

Hyperbola derives from the Greek word uperbolh which means “excessive.” We call deliberate and obvious exaggeration hyperbole. What’s excessive about a hyperbola?

Well, it turns out that Apollonius of Perga, the Greek who wrote about Conic Sections in the 2nd and 3rd centuries BC, compared other curves to the circle. All points on the circle are the same distance from its center. The circle is defined as not having any eccentricity; other curves are rated for their eccentricity. How wonderful is that? I come from a long line of eccentrics, myself, but I hadn’t thought about how that means we are pushing the curve out of its circular orbit. We’re not square pegs trying to fit into round holes. We’re actually stretching the holes to fit us!

So. A circle has zero eccentricity. An ellipse has an eccentricity between zero and one. (In Greek, ellipse means deficient!) A parabola has an eccentricity of one. (In Greek, parabola means comparable.) And those crazy hyperbolas are the most eccentric with their eccentricities that exceed one. (How excessive can you get?)

My earrings clearly fall into the excessive category with those swirls of crocheted green and tufts of teal jutting out from the lilac base. They were made of recycled cashmere and silk yarn by Sandy Meeks who sells her wares at www.meekssandygirl.etsy.com.

To make hyperbolic crochet that curves eccentrically, you just add stitches at regular intervals. How does this connect to my day? Today our math consultant Monica Neagoy visited my classroom. Watching her teach is an inspiration! She taught the culminating lesson in our investigation of repeating patterns. Hyperbolic shapes form when you follow a repeating pattern of increase. QED.

Addendum: I think mathematicians should examine curly hair like that of Apollonius. Hyperbolic? Truly!

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